Thermodynamics and evaporation of the (2+1)-dimensional black hole

The properties of cannonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in three dimensions (3D) are studied. In 3D Einstein–anti–de Sitter gravity we have two relevant mass scales, ${\mathit{m}}_{\mathit{c}}$=1/G and ${\mathit{m}}_{\mathit{P}}$=(${\mathrm{ħ}}^2$Λ/G${)}^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the ‘‘weak coupling’’ regime ΛG${)}^{\mathrm{-}2}$, the end point of an evaporating black hole formed with an initial mass ${\mathit{m}}_0$>${\mathit{m}}_{\mathit{P}}$ is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the ‘‘strong coupling’’ regime Λ>(ħG${)}^{\mathrm{-}2}$, a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti–de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy, black hole states are locally stable. In the weak coupling regime black hole states are more probable than pure radiation states.